Relevant bibliographies by topics / Fractal mathematics

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Fractal mathematics'

Author: Grafiati
Published: 3 June 2025
Last updated: 31 July 2025

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Journal articles on the topic "Fractal mathematics"

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Alghar, Muhammad Zia, Natasya Ziana Walidah, and Marhayati Marhayati. "Ethnomathematics: The exploration of fractal geometry in Tian Ti Pagoda using the Lindenmayer system." Alifmatika: Jurnal Pendidikan dan Pembelajaran Matematika 5, no. 1 (2023): 57–69. http://dx.doi.org/10.35316/alifmatika.2023.v5i1.57-69.

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This study explores the concept of fractal geometry found in the Tian Ti Pagoda. Fractal geometry is a branch of mathematics describing the properties and shapes of various fractals. A qualitative method with an ethnographic approach is used in this study. Observation, field notes, interviews, documentation, and literature study obtained research data. The observation results were processed computationally using the Lindenmayer system method via the L-Studio application to view fractal shapes. The results show that the concept of fractal geometry is contained in the ornaments on the Tian Ti Pa
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Siegrist, Raymond. "Activities for Students: Inquiry into Fractals." Mathematics Teacher 103, no. 3 (2009): 206–12. http://dx.doi.org/10.5951/mt.103.3.0206.

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The exotic images of fractals often pique the interest of high school mathematics students, and this interest presents an opportunity for geometry teachers to draw students into an investigation of transformations and patterns. By using a simple building block and fractals' self-imaging characteristic (as the figure grows, it retains the pattern established by the building block), teachers can bring construction of fractals into the high school geometry curriculum. The three activities described in this article engage students in constructing a fractal, searching a fractal for patterns, and us
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Siegrist, Raymond. "Activities for Students: Inquiry into Fractals." Mathematics Teacher 103, no. 3 (2009): 206–12. http://dx.doi.org/10.5951/mt.103.3.0206.

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The exotic images of fractals often pique the interest of high school mathematics students, and this interest presents an opportunity for geometry teachers to draw students into an investigation of transformations and patterns. By using a simple building block and fractals' self-imaging characteristic (as the figure grows, it retains the pattern established by the building block), teachers can bring construction of fractals into the high school geometry curriculum. The three activities described in this article engage students in constructing a fractal, searching a fractal for patterns, and us
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Camp, Dane R. "A Fractal Excursion." Mathematics Teacher 84, no. 4 (1991): 265–75. http://dx.doi.org/10.5951/mt.84.4.0265.

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Recently, chaos theory and the related topic of fractal geometry have blossomed as creative fields of study in mathematics and physics. Fractals are shapes containing self-similarity on arbitrary magnification. One such object, the Koch curve, is generated by simple recursion on an equilateral triangle. The process used to produce the curve is a great way to introduce students to some concepts of fractal geometry.
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MITINA, OLGA V., and FREDERICK DAVID ABRAHAM. "THE USE OF FRACTALS FOR THE STUDY OF THE PSYCHOLOGY OF PERCEPTION: PSYCHOPHYSICS AND PERSONALITY FACTORS, A BRIEF REPORT." International Journal of Modern Physics C 14, no. 08 (2003): 1047–60. http://dx.doi.org/10.1142/s0129183103005182.

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The present article deals with perception of time (subjective assessment of temporal intervals), complexity and aesthetic attractiveness of visual objects. The experimental research for construction of functional relations between objective parameters of fractals' complexity (fractal dimension and Lyapunov exponent) and subjective perception of their complexity was conducted. As stimulus material we used the program based on Sprott's algorithms for the generation of fractals and the calculation of their mathematical characteristics. For the research 20 fractals were selected which had differen
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TREGUBOVA, I. A. "FRACTAL GRAPHICS FOR VIRTUAL ENVIRONMENT GENERATION." Digital Technologies 26 (2019): 29–35. http://dx.doi.org/10.33243/2313-7010-26-29-35.

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Progress in hardware and software development is impressively fast. The main reason of computer graphics fast improvement is a full experience that can be reached though visual representation of our world. Therefore, the most interesting problem of it is a realistic image with high quality and resolution, which often requires procedural graphics generation. The article analyzes simplicity of a fractal and mathematics abstraction. Mathematics describes not only accuracy and logic but also beauty of the Universe. Mountains, clouds, trees, cells do not fit into the world of Euclidean geometry. Th
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Жихарев, Л., and L. Zhikharev. "Fractals In Three-Dimensional Space. I-Fractals." Geometry & Graphics 5, no. 3 (2017): 51–66. http://dx.doi.org/10.12737/article_59bfa55ec01b38.55497926.

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It has long been known that there are fractals, which construction resolve into cutting out of elements from lines, curves or geometric shapes according to a certain law. If the fractal is completely self-similar, its dimensionality is reduced relative to the original object and usually becomes fractional. The whole fractal is often decomposing into a set of separate elements, organized in the space of corresponding dimension. German mathematician Georg Cantor was among the first to propose such fractal set in the late 19th century. Later in the early 20th century polish mathematician Vaclav S
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Sergeeva, Larisa. "THE USE OF FRACTAL GEOMETRY ELEMENTS AS A MEANS OF AESTHETIC EDUCATION OF PRIMARY SCHOOL STUDENTS." SOCIETY. INTEGRATION. EDUCATION. Proceedings of the International Scientific Conference 3 (May 20, 2020): 562. http://dx.doi.org/10.17770/sie2020vol3.4934.

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Currently, the issue of aesthetic education is becoming one of the key issues in the field of education. The relevance of the article is due to the fact that mathematics has great aesthetic potential, which is not always revealed in the process of teaching mathematics in elementary school. An important role in revealing the beauty of mathematical content in elementary school is played by the familiarity of schoolchildren with a young rapidly developing mathematical field - fractal geometry. In order to prove the effectiveness of using fractal geometry elements for the formation of aesthetic re
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LAI, PENG-JEN. "HOW TO MAKE FRACTAL TILINGS AND FRACTAL REPTILES." Fractals 17, no. 04 (2009): 493–504. http://dx.doi.org/10.1142/s0218348x09004533.

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Intensive research on fractals began around 1980 and many new discoveries have been made. However, the connection between fractals, tilings and reptiles has not been thoroughly explored. This paper shows that a method, similar to that used to construct irregular tilings in ℜ2 can be employed to construct fractal tilings. Five main methods, including methods in Escher style paintings and the Conway criterion are used to create the fractal tilings. Also an algorithm is presented to generate fractal reptiles. These methods provide a more geometric way to understand fractal tilings and fractal rep
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LAPIDUS, MICHEL L. "FRACTALS AND VIBRATIONS: CAN YOU HEAR THE SHAPE OF A FRACTAL DRUM?" Fractals 03, no. 04 (1995): 725–36. http://dx.doi.org/10.1142/s0218348x95000643.

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We study various aspects of the question “Can one hear the shape of a fractal drum?”, both for “drums with fractal boundary” (or “surface fractals”) and for “drums with fractal membrane” (or “mass fractals”).
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Dissertations / Theses on the topic "Fractal mathematics"

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McClure, Mark. "Fractal measures on infinite-dimensional sets /." The Ohio State University, 1994. http://rave.ohiolink.edu/etdc/view?acc_num=osu148785391310164.

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Liao, Haoke. "Fractal simulation of plants." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-91410.

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We study two methods of simulation of plants in R2 , the Lindenmayer system and the iterated function system. The algorithm for a L-system simulates fast and efficiently the growth structure of the plants. The iterated function system can be done by deterministic iteration or by the so called chaos game.
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Donovan, George C. "Fractal functions, splines, and wavelet." Diss., Georgia Institute of Technology, 1995. http://hdl.handle.net/1853/30411.

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Mullins, Edmond N. "Derivation bases, interval functions, and fractal measures /." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487942182325914.

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Wessel, Ralf. "Formation and flow of fractal aggregates." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240023.

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Blunt, Martin Julian. "The growth and properties of fractal boundaries." Thesis, University of Cambridge, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293638.

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Piacquadio, Losada Maria N. "P.D.E. in planar regions with fractal boundary." Thesis, University of Warwick, 1988. http://wrap.warwick.ac.uk/91885/.

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Xiao, Yimin. "Fractal Measures and Related Properties of Gaussian Random Fields /." The Ohio State University, 1996. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487935573769563.

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Peng, Na. "Fractal Gauges for Hyperspace: One Limit Point." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1278387275.

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Cesbron, Fred́eŕique Chantal. "Multiresolution fractal coding of still images." Diss., Georgia Institute of Technology, 1997. http://hdl.handle.net/1853/15508.

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Books on the topic "Fractal mathematics"

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Dauphiné, André. Fractal geography. Wiley, 2011.

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Falconer, K. J. Fractal Geometry. John Wiley & Sons, Ltd., 2003.

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1955-, Haight Robert G., Leary Rolfe A, and North Central Forest Experiment Station (Saint Paul, Minn.), eds. The fractal forest: Fractal geometry and applications in forest science. North Central Forest Experiment Station, 1994.

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Lorimer, Nancy D. The fractal forest: Fractal geometry and applications in forest science. North Central Forest Experiment Station, Forest Service, U.S. Dept. of Agriculture, 1994.

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Davide, La Torre, Mendivil Franklin, and Vrscay Edward R, eds. Fractal-based methods in analysis. Springer, 2012.

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Siegfried, Graf, and Zähle Martina, eds. Fractal Geometry and Stochastics II. Birkhäuser Basel, 2000.

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Falconer, K. J. Fractal geometry: Mathematical foundations and applications. 2nd ed. Wiley, 2003.

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Falconer, K. J. Fractal geometry: Mathematical foundations and applications. Halsted Press, 2003.

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Falconer, K. J. Fractal geometry: Mathematical foundations and applications. Wiley, 2014.

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M, Blackledge J., Evans A. K, Turner Martin J, and Institute of Mathematics and Its Applications, eds. Fractal geometry: Mathematical methods, algorithms, applications. Horwood Pub. for the Institute of Mathematics and its Applications, 2002.

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Book chapters on the topic "Fractal mathematics"

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Li, Liangliang, Yu Huang, and Goong Chen. "Fractal." In Synthesis Lectures on Mathematics & Statistics. Springer Nature Switzerland, 2025. https://doi.org/10.1007/978-3-031-84828-5_8.

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Edgar, Gerald A. "Fractal Examples." In Undergraduate Texts in Mathematics. Springer New York, 1990. http://dx.doi.org/10.1007/978-1-4757-4134-6_1.

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Waters, Thomas. "Fractal Geometry." In The Four Corners of Mathematics. A K Peters/CRC Press, 2024. http://dx.doi.org/10.1201/9781003455592-4.

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Lapidus, Michel L., and Machiel van Frankenhuijsen. "Fractal Tube Formulas." In Springer Monographs in Mathematics. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-2176-4_8.

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Rataj, Jan, and Martina Zähle. "Fractal Versions of Curvatures." In Springer Monographs in Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-18183-3_10.

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Sander, Leonard M. "Fractal Growth Processes." In Mathematics of Complexity and Dynamical Systems. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1806-1_28.

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Cho, Shinil. "Chaos and Fractal." In Synthesis Lectures on Mathematics & Statistics. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-33886-1_6.

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Hunt, Fern, and Francis Sullivan. "Methods of computing fractal dimensions." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0086754.

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Kaplan, Daniel, and Leon Glass. "Self-Similarity and Fractal Geometry." In Texts in Applied Mathematics. Springer New York, 1995. http://dx.doi.org/10.1007/978-1-4612-0823-5_3.

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Schmeling, Jörg. "Ergodic TheoryFractal geometry ergodic theory : Fractal GeometryErgodic theory fractal geometry." In Mathematics of Complexity and Dynamical Systems. Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-1806-1_18.

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Conference papers on the topic "Fractal mathematics"

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Chand, A. K. B., and P. Viswanathan. "Cubic hermite and cubic spline fractal interpolation functions." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756439.

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MANDELBROT, BENOIT B. "SELECTED TOPICS IN MATHEMATICS, PHYSICS, AND FINANCE ORIGINATING IN FRACTAL GEOMETRY." In Fractals and Related Phenomena in Nature. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702746_0001.

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Agapie, Alina Laura, Marinel Nicolae Horablaga, Gabriela Gorinoiu, and Florin Sala. "Fractal analysis for soybean leaves characterization." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0026508.

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Serdyukov, V. I., N. A. Serdyukova, and S. I. Shishkina. "Quasi-fractal models of system sustainability." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2021. AIP Publishing, 2023. http://dx.doi.org/10.1063/5.0163667.

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Bedabrata Chand, Arya Kumar. "Natural Bicubic Spline Coalescence Fractal Interpolation Function." In Annual International Conference on Computational Mathematics, Computational Geometry & Statistics. Global Science and Technology Forum (GSTF), 2012. http://dx.doi.org/10.5176/2251-1911_cmcgs53.

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Safitri, Diah Wahyu, and Dwi Juniati. "Classification of diabetic retinopathy using fractal dimension analysis of eye fundus image." In INTERNATIONAL CONFERENCE ON MATHEMATICS: PURE, APPLIED AND COMPUTATION: Empowering Engineering using Mathematics. Author(s), 2017. http://dx.doi.org/10.1063/1.4994414.

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Su, Weiyi. "Some problems in fractal differential equations." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4952039.

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Kolcun, Alexej. "Remarks to BCM for fractal dimension computation." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5043713.

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Zhao, Haixia, and Shoucheng Wang. "Application of Fractal Mathematics in Mode Recognition and Image Processing." In 2011 International Conference on Measuring Technology and Mechatronics Automation (ICMTMA). IEEE, 2011. http://dx.doi.org/10.1109/icmtma.2011.136.

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Roychowdhury, Mrinal K. "Preface of the "Symposium on fractal geometry, quantization dimension and related topics"." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756437.

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